# The decay of a neutron

This project must be done by individuals.

For the purposes of this exercise, you may treat the neutrino and anti-neutrino as massless. In other words, they have no rest mass, but they do have energy and they do carry momentum.

An isolated neutron is not stable. It decays into three particles:

• a proton
• an electron
• an anti-neutrino

Fill in the table below. Note that I have set the mass of the anti-neutrino to be zero, which is a simplifying approximation.

```  particle            mass (kg)          mass (MeV/c^2)
---------------------------------------------------

neutron

proton

electron

anti-neutrino           0                   0

---------------------------------------------------
```

1. What is the difference in mass between the initial neutron and the final products?
2. How much energy does this correspond to?

Assume that the neutron is initially motionless. Suppose that after the decay, the proton is likewise motionless. The anti-neutrino, of course, can't be motionless, so it flies off at the speed of light to the right, in the positive x-direction.

3. Draw a pair of pictures showing the "Before" and "After" arrangement of the particles, and their motions.
4. Write an equation for the total energy of the particles in the "After" set.
5. Write an equation for the total momentum of the particles in the "After" set.
6. How fast must the electron fly away from the proton? Express your answer as a fraction of the speed of light.

(Hint: the algebra in this problem isn't trivial. Feel free to solve for the electron's speed numerically, as long as you describe your method.)